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Q. 17

Found in: Page 860


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Short Answer

What is the dot product of the vector functions r1(t)=x1(t), y1(t) and r2(t)=x2(t), y2(t)?

The dot product of the given two vector functions is x1(t)x2(t)+y1(t)y2(t).

See the step by step solution

Step by Step Solution

Step 1. Given Information.

The given vector functions are r1(t)=x1(t), y1(t) and r2(t)=x2(t), y2(t).

Step 2. Find the dot product.

Let's find the dot product,

r1t·r2t=x1(t), y1(t)·x2(t), y2(t)=x1(t)i+y1(t)j·x2(t)i+ y2(t)j=x1(t)x2(t)i·i+x1(t)y2(t)i·j+y1(t)x2(t)j·i+y1(t)y2(t)j·jSince i·i=1, i·j=0, j·i=0, j·j=1=x1(t)x2(t)+y1(t)y2(t)

Thus, the product of two vector functions is a scalar function.

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